I’ve got it looking the way I want! Here’s what I did:
1. I used Omar’s suggestion to cheat along with Martin’s Roughness and Color ideas. I made the grille material blue instead of dark gray and I dropped the transmission value and increased the roughness.


2. Martin’s node tree example got me thinking about Math nodes and Mix Color nodes, which led me to a Blur Any Texture tutorial on YouTube by Ryan King Art. The blur node group and the whole material node setup is below. I connected the image texture to the Emission channel of the Principled BSDF shader (which I forgot to do originally) and I balanced the Strength value of the PBSDF shader against the Strength of the Emission shader. I got rid of the Layer Weight node and just used a Fresnel node.


The result:

